London to Edinburgh late July 2014 - how to get there and where to stop?

For #2, I'd suggest York, since it's on the mainline from London to Edinburgh. Great railway museum (free), the Shambles, you can walk the Walls around the city, visit York Minster (and go up in the tower for city views). Lots to do there.

I'd suggest York too, spend two nights there. The railway museum is right by the station. The medieval center is a short walk, much of it pedestrian. York Minster is one of Britain's best cathedrals, evensong is a great experience. You can walk along the city walls. The Yorkshire Museum is excellent for prehistory and natural history. The abbey ruins next to the museum are lovely. The York Castle Museum tells a lot about life in York though the centuries. We didn't visit Jorvik, which is a "living history" exhibit about the Norse period in Yorkshire. Also we skipped the Richard III museum, reportedly pretty hokey.

There's a great deal to see potentially between London and Edinburgh, obviously. I suggest putting all your free time into York because I think it makes more sense to spend both nights in one place instead of packing/unpacking twice, and because York is so compact and easy on foot from the train. It probably offers the most sightseeing value for the least expenditure of time and energy along your way.

Good luck with the castle, have fun!

Many of your queries were answered recently when someone had a similar question. https://community.ricksteves.com/travel-forum/england/train-tips-london-to-edinburgh

I think direct flight exist between Canada & Edinburgh. (Check Air Canada / Air Transat).

York is the place to have a stopover on the East Coast Main Line.

It looks pretty easy to apply the RailCard discount when purchasing through www.nationalrail.co.uk, on top of the advance rates. On the price results list, you can click on "other prices" to see how much the additional discount is. Obviously, if the shopping cart requires you to enter a RailCard number before check-out, then that won't work, but I don't see any such requirement on the East Coast Line booking system.

Traditionally railcards in the UK had to be presented at the point of booking, otherwise the transaction could not continue.

I'd agree with the others, of the cities you mentioned it would have to be York if you've never been before. If you want to stay in a castle your best chance on the route you are going is Northumberland in England or Scottish Borders in Scotland, simply because fewer people tend to go there.

If booking ahead you can indicate which railcard you have to get the discount.
No ref.numbers or IDs will be asked for
Get the card issued at a manned mainline station once in the UK,
You must have the card and tickets together at all times while travelling

I haven't been to the other places on your list, but like the others I highly recommend York.

If you book ASAP (about 12 weeks in advance) on the East Coast site, you can get discount fare tickets for London-York and York-Edinburgh. And because you are a group of four, you can get 1/3 more off the discount fare. The lowest possible fares for all four of you together are £38.40 for London-York and £44.40 for York-Edinburgh. And you won't have to buy a Railcard. There is a limited number of seats at each discount fare level so book as soon as the window opens or the cheapest seats will be gone. As of today booking is open through 18 July.

I am interested in these answers as well. I am wondering if the esteemed posters here would have him consider a Britrail pass? I think if the girls are under a certain age (like 15 or 16?), they ride free with parents. I am trying to figure out my rail needs as well and after purchasing the Friends and Family rail card (50 GBP) and then having to pay for both myself and my daughter for all of our trips (Wales, York, Edinburgh) it seems cheaper. Or am I just dreaming?

For adults at least,if you have a plan and buy Advance tickets I think the cost would he about 1/2 the britrail passes.
I was looking the other day for 5 trips,inc Edinburgh, Stratford,Oxford ,Leeds ,York andHolyhead,and even "pay on the day" off peak tickets were cheaper than the pass, BUT that was 2adults and included buying a Two Together Pass.
If you are prebooking accom. ,booking travel kinda follows.
Advance makes sense on long leg trips,not so much on 20mile hops.
Friends and Family card is £30